1 a 2 points Approximate each integral using the composite t

1. (a) 2 points] Approximate each integral using the composite trapezoidal rule with the number of sub-interval M 10. (b) [2 points] Approximate each integral using the composite Simpson rule with M 5. 11+x2 2. [2 points] Use Gauss-Legendre integration to show that two integrals are equivalent. sin (t) dt sin(x 1) dx 3. The three point Gauss-Legendre rule is (a) l point) verify this by GLTable. (b) [3 points] Show that the formula is exact for fx) 1, x,x2, x3, x x5. Hint: If fis an odd function, the integral offover [-1,ijis zero

Solution

import win32com.client sh=win32com.client.gencache.EnsureDispatch(\'Shell.Application\',0) ns = sh.NameSpace(r\'m:\\music\\Aerosmith\\Classics Live!\') colnum = 0 columns = [] while True: colname=ns.GetDetailsOf(None, colnum) if not colname: break columns.append(colname) colnum += 1 for item in ns.Items(): print (item.Path) for colnum in range(len(columns)): colval=ns.GetDetailsOf(item, colnum) if colval: print(\'\\t\', columns[colnum], colval)